ON SPRINDŽUK’S CLASSIFICATION OF -ADIC NUMBERS
Abstract We carry Sprindžuk’s classification of the complex numbers to the field $\mathbb{Q}_{p}$ of $p$ -adic numbers. We establish several estimates for the $p$ -adic distance between $p$ -adic roots of integer polynomials, which we apply to show that almost all $p$ -adic numbers, with respect to...
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| Published in | Journal of the Australian Mathematical Society (2001) Vol. 111; no. 2; pp. 221 - 231 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Canberra
Cambridge University Press
01.10.2021
|
| Subjects | |
| Online Access | Get full text |
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| Abstract | Abstract
We carry Sprindžuk’s classification of the complex numbers to the field
$\mathbb{Q}_{p}$
of
$p$
-adic numbers. We establish several estimates for the
$p$
-adic distance between
$p$
-adic roots of integer polynomials, which we apply to show that almost all
$p$
-adic numbers, with respect to the Haar measure, are
$p$
-adic
$\tilde{S}$
-numbers of order 1. |
|---|---|
| AbstractList | Abstract
We carry Sprindžuk’s classification of the complex numbers to the field
$\mathbb{Q}_{p}$
of
$p$
-adic numbers. We establish several estimates for the
$p$
-adic distance between
$p$
-adic roots of integer polynomials, which we apply to show that almost all
$p$
-adic numbers, with respect to the Haar measure, are
$p$
-adic
$\tilde{S}$
-numbers of order 1. We carry Sprindžuk’s classification of the complex numbers to the field \(\mathbb{Q}_{p}\) of \(p\)-adic numbers. We establish several estimates for the \(p\)-adic distance between \(p\)-adic roots of integer polynomials, which we apply to show that almost all \(p\)-adic numbers, with respect to the Haar measure, are \(p\)-adic \(\tilde{S}\)-numbers of order 1. |
| Author | BUGEAUD, YANN KEKEÇ, GÜLCAN |
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| Cites_doi | 10.1515/crll.1932.166.118 10.1017/CBO9780511542886 10.1007/978-3-662-11569-5 10.1090/surv/019 10.1007/s11139-005-0822-8 10.1112/S0025579300000231 |
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| Copyright | 2019 Australian Mathematical Publishing Association Inc. |
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| DOI | 10.1017/S1446788719000454 |
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| References | S1446788719000454_r6 Diaz (S1446788719000454_r7) 1991; 13 Amou (S1446788719000454_r1) 1996; 470 Sprindžuk (S1446788719000454_r10) 1962; 2 S1446788719000454_r12 Mahler (S1446788719000454_r8) 1932; 166 Mahler (S1446788719000454_r9) 1935; 3 Sprindžuk (S1446788719000454_r11) 1969 S1446788719000454_r3 Amou (S1446788719000454_r2) 1996 S1446788719000454_r5 S1446788719000454_r4 |
| References_xml | – volume: 166 start-page: 118 year: 1932 ident: S1446788719000454_r8 article-title: Zur Approximation der Exponentialfunktionen und des Logarithmus. I, II publication-title: J. reine angew. Math. doi: 10.1515/crll.1932.166.118 contributor: fullname: Mahler – ident: S1446788719000454_r5 doi: 10.1017/CBO9780511542886 – ident: S1446788719000454_r12 doi: 10.1007/978-3-662-11569-5 – ident: S1446788719000454_r6 doi: 10.1090/surv/019 – volume: 3 start-page: 177 year: 1935 ident: S1446788719000454_r9 article-title: Über eine Klasseneinteilung der p-adischen Zahlen publication-title: Mathematica (Leiden) contributor: fullname: Mahler – start-page: 112 volume-title: Analytic Number Theory (Kyoto, 1995) year: 1996 ident: S1446788719000454_r2 contributor: fullname: Amou – ident: S1446788719000454_r3 doi: 10.1007/s11139-005-0822-8 – volume: 470 start-page: 27 year: 1996 ident: S1446788719000454_r1 article-title: On Sprindžuk’s classification of transcendental numbers publication-title: J. reine angew. Math. contributor: fullname: Amou – ident: S1446788719000454_r4 doi: 10.1112/S0025579300000231 – volume-title: Mahler’s Problem in Metric Number Theory year: 1969 ident: S1446788719000454_r11 contributor: fullname: Sprindžuk – volume: 13 start-page: 131 year: 1991 ident: S1446788719000454_r7 article-title: Passage d’une mesure d’approximation à une mesure de transcendance publication-title: C. R. Math. Rep. Acad. Sci. Canada contributor: fullname: Diaz – volume: 2 start-page: 215 year: 1962 ident: S1446788719000454_r10 article-title: On a classification of transcendental numbers publication-title: Litovsk. Mat. Sb. contributor: fullname: Sprindžuk |
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| Snippet | Abstract
We carry Sprindžuk’s classification of the complex numbers to the field
$\mathbb{Q}_{p}$
of
$p$
-adic numbers. We establish several estimates for the... We carry Sprindžuk’s classification of the complex numbers to the field \(\mathbb{Q}_{p}\) of \(p\)-adic numbers. We establish several estimates for the... |
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| Title | ON SPRINDŽUK’S CLASSIFICATION OF -ADIC NUMBERS |
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